Dual diffeomorphisms and finite distance asymptotic symmetries in 3d gravity

Geiller, Marc; Goeller, Christophe

doi:10.48550/arxiv.2012.05263

Cited by 3 publications

(5 citation statements)

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“…see [37,[69][70][71][72][73][74][75][76][77][78], gravitational observables [79], and more generally, to the characterization of asymptotic symmetries in gauge and gravitational subsystems, see e.g. [28,35,68,[80][81][82][83][84][85][86][87]. Our work revisits such constructions, from the vantage point of a global field space of solutions in a spacetime M ∪ M , where M is the complementary spacetime region of M .…”

Section: Jhep02(2022)172mentioning

confidence: 99%

“…where [•, •] is to be understood as the Lie-bracket on field-space forms. 35 As in finite dimensions, one can understand this equation as a flatness condition for a field-space gauge potential −δU U −1 = U δU −1 . 36 The Maurer-Cartan form also transforms nicely under field-dependent gauge transformations, namely:…”

Section: Jhep02(2022)172mentioning

confidence: 99%

“…By focusing on the (pre-)symplectic geometry underlying post-selection, we will be readily able to connect our work to previous literature on edge modes. 35 That is, [ω1, ω2] := ω1ω2 − (−1) pq ω2ω1 if ω1 is a p-form and ω2 a q-form (as before, the field-space wedge product is kept implicit).…”

Section: Symplectic Geometry Of Splitting Post-selectionmentioning

confidence: 99%

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Edge modes as reference frames and boundary actions from post-selection

Carrozza

Hoehn

2022

J. High Energ. Phys.

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We introduce a general framework realizing edge modes in (classical) gauge field theory as dynamical reference frames, an often suggested interpretation that we make entirely explicit. We focus on a bounded region M with a co-dimension one time-like boundary Γ, which we embed in a global spacetime. Taking as input a variational principle at the global level, we develop a systematic formalism inducing consistent variational principles (and in particular, boundary actions) for the subregion M. This relies on a post-selection procedure on Γ, which isolates the subsector of the global theory compatible with a general choice of gauge-invariant boundary conditions for the dynamics in M. Crucially, the latter relate the configuration fields on Γ to a dynamical frame field carrying information about the spacetime complement of M; as such, they may be equivalently interpreted as frame-dressed or relational observables. Generically, the external frame field keeps an imprint on the ensuing dynamics for subregion M, where it materializes itself as a local field on the time-like boundary Γ; in other words, an edge mode. We identify boundary symmetries as frame reorientations and show that they divide into three types, depending on the boundary conditions, that affect the physical status of the edge modes. Our construction relies on the covariant phase space formalism, and is in principle applicable to any gauge (field) theory. We illustrate it on three standard examples: Maxwell, Abelian Chern-Simons and non-Abelian Yang-Mills theories. In complement, we also analyze a mechanical toy-model to connect our work with recent efforts on (quantum) reference frames.

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Section: Jhep02(2022)172mentioning

confidence: 99%

Section: Jhep02(2022)172mentioning

confidence: 99%

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Edge modes as reference frames and boundary actions from post-selection

Carrozza

Hoehn

2022

J. High Energ. Phys.

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“…The equations of motion therefore combine to give once again J = 0 and P = 0. It is very intriguing that this mechanism is the same as in three-dimensional gravity, where the BMS 3 central charge c 1 (or a chiral mismatch c + = c − between the two Brown-Henneaux central charges in the AdS 3 case) can be switched on by adding a Chern-Simons and a torsion term (together these constitute Witten's exotic Lagrangian [60]) to the first order Lagrangian, without however modifying the equations of motion [61][62][63].…”

Section: 1b)mentioning

confidence: 99%

BMS₃ mechanics and the black hole interior

Geiller¹,

Livine²,

Sartini³

2021

Class. Quantum Grav.

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The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein–Hilbert action reduces to a one-dimensional mechanical model. We have shown in [1] that this model exhibits a symmetry under the (2+1)-dimensional Poincaré group. Here we extend the Poincaré transformations to the inﬁnite-dimensional BMS3 group. Although the black hole model is not invariant under those extended transformations, we can write it as a geometric action for BMS3, where the conﬁguration space variables are elements of the algebra bms3 and the equations of motion transform as coadjoint vectors. The BMS3 symmetry breaks down to its Poincaré subgroup, which arises as the stabilizer of the vacuum orbit. This symmetry breaking is analogous to what happens with the Schwarzian action in AdS2 JT gravity, although in the present case there is no direct interpretation in terms of boundary symmetries. This observation, together with the fact that other lower-dimensional gravitational models (such as the BTZ black hole) possess the same broken BMS3 symmetries, provides yet another illustration of the ubiquitous role played by this group.

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“…The BMS algebra can then be recovered as a sub-algebra, within the enveloping loop algebra, preserving a restricted set of boundary conditions, as shown in details in appendix. See also [44,45] for more details.…”

Section: A Classical Boundary Charges As a Current Algebramentioning

confidence: 99%

The Quantum Gravity Disk: Discrete Current Algebra

Freidel,

Goeller,

Livine

2021

Preprint

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We study the quantization of the corner symmetry algebra of 3d gravity associated with 1d spatial boundaries. We first recall that in the continuum, this symmetry algebra is given by the central extension of the Poincaré loop algebra. At the quantum level, we construct a discrete current algebra with a DSU(2) quantum symmetry group that depends on an integer N . This algebra satisfies two fundamental properties: First it is compatible with the quantum space-time picture given by the Ponzano-Regge state-sum model, which provides a path integral amplitudes for 3d loop quantum gravity. We then show that we recover in the N → ∞ limit the central extension of the Poincaré current algebra. The number of boundary edges defines a discreteness parameter N which counts the number of flux lines attached to the boundary. We analyse the refinement, coarse-graining and fusion processes as N changes. Identifying a discrete current algebra on quantum boundaries is an important step towards understanding how conformal field theories arise on spatial boundaries in loop quantum gravity. It also shows how an asymptotic BMS symmetry group could appear from the continuum limit of 3d quantum gravity. Contents B. Commutators of the tentative discrete Virasoro operators Dn

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Dual diffeomorphisms and finite distance asymptotic symmetries in 3d gravity

Cited by 3 publications

References 75 publications

Edge modes as reference frames and boundary actions from post-selection

Edge modes as reference frames and boundary actions from post-selection

BMS₃ mechanics and the black hole interior

The Quantum Gravity Disk: Discrete Current Algebra

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Dual diffeomorphisms and finite distance asymptotic symmetries in 3d gravity

Cited by 3 publications

References 75 publications

Edge modes as reference frames and boundary actions from post-selection

Edge modes as reference frames and boundary actions from post-selection

BMS3 mechanics and the black hole interior

The Quantum Gravity Disk: Discrete Current Algebra

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Product

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BMS₃ mechanics and the black hole interior